Must admit that the original post with the "123" idea, was put up with a few glasses of wine in me, just to throw the cat among the pigeons and see what sort of reaction it got. I actually wanted to post the "135" idea, but it seemed way too radical.
I'm not much of a mathematician, and at the moment the 3 numbers that might be used to score such tounaments could perhaps be disregarded. Is there any strength of feeling out there at all, in support of the concept of scoring a tournament in such a way that it is recognised that there are 3 possible ends to a game?
I may be wrong, but it seems to me that it is fairly widely excepted that it is easier to win as white than as black. Surely a black win is therefore more valuable, and should therefore be scored higher. The reason that black often plays for a draw is that a black win is not given the value it deserves. Tounaments would be far more decisive, and games would be far more exciting, if the scoring better reflected the nature of the game.
Regarding the concept of awarding a point to only black (i.e. nothing to white) if a game is drawn: if you accept above premise that a win is easier for white than black, then you have to also accept that a draw is more difficult for black to achieve than for white to achieve.
I don't know a great deal about chess, and I am absolutely 100 percent new to the concept of a chess tournament, but one thing I notice straight away, is that chess has the chance to do what football ("soccer" for you colonials) can't, i.e. fight against the "boring draw" problem. Football can't, because "home" and "away" are not always clearly defined, but in chess there is always a black and a white.